Abstract Biophysical properties can be computer-modeled using quantum mechanics (QM). While vastly more computationally costly than molecular mechanics (MM), QM methods are essential for bond-breaking and/or high accuracy. Indeed, QM methods have advanced with exciting, (and ongoing) improvements in the accuracy of density functional theory (DFT). These DFT improvements could open new applications opportunities reliable conformational searching, molecular recognition, ligand binding, enzymology modeling, and all the areas where QM simulations can aid biophysical chemistry. However, the latest density functionals require very large and computationally demanding basis sets to attain their high accuracy. Use of smaller basis sets leads to unconverged results with often unacceptable errors in relative energies, so only small systems can be treated at present with high accuracy DFT calculations. This proposal addresses the unmet need to reduce the computational cost of achieving large basis set accuracy in DFT calculations. Its first innovation is the use of minimal adaptive basis functions (MAB) for this purpose. The MAB is a small (minimal) set of functions, adaptively formed in situ from a traditional large basis via an atom-blocked, sparse transformation. The DFT calculation is performed in the MAB, followed by a single-shot perturbative correction. MAB accuracy has been shown to be virtually indistinguishable from a conventional large basis calculation on biophysically relevant examples, while analysis suggests the potential for more than an order-of-magnitude speedup. A second innovation to further extend the size of MAB-DFT calculations is a new MAB-based QM-in-QM method that exactly embeds a smaller active QM region described by a large basis into a larger QM environment that is pre- optimized in a smaller basis set. Large QM regions have been argued to be essential in QM/MM. The Phase II research has three principal objectives that together will bring the MAB-DFT method up to the level of application-ready software. First, the software implementation of the MAB-DFT method will be optimized to remove current bottlenecks, and to take full advantage of the block-sparse structure of the MAB in order to achieve the speedups the method is capable of yielding. This requires careful consideration of matrix element evaluation, numerical quadrature and linear algebra across all five steps in a MAB-DFT calculation. Second, the proposed MAB-based QM-in-QM embedding model will be implemented, using all optimizations from the first aim, as well as exact replacement of the environment by an effective core potential-like term. Third, timings and accuracy tests of both stand-alone MAB-DFT and QM-in-QM MAB-DFT calculations will be conducted and reported for a range of biophysically relevant energy differences in both model and realistic systems. Additionally, some model applications drawn from areas such drug design, enzymology and DNA/RNA chemistry will be performed.